Free vibration response of internally-thickness-tapered laminated composite square plates based on an energy method

Abstract

In the present work, the free vibration response of symmetric linearly-thickness-tapered laminated composite square plates is considered for a variety of taper configurations. Since exact and closed-form solutions for the natural frequencies and mode shapes of the plates could not be obtained from the corresponding complex partial differential equations in space and time coordinates, the Ritz method in conjunction with the Classical Laminated Plate Theory (CLPT) and then the First-order Shear Deformation Theory (FSDT) is used to obtain the system’s mass and stiffness matrices for out-of-plane bending vibrations. The free vibration analysis of the plates is conducted using these system matrices and the natural frequencies and mode shapes are determined. Different boundary conditions are considered for the free vibration response of the plates and the computational work is performed in the MATLAB® environment. The convergence of the series expansions used for the out-of-plane displacement functions and the Ritz solutions for plates with various boundary conditions are established. The demonstration of solution accuracy is performed by conducting a so-called “layer reduction test” and also by comparing the results obtained by using the Ritz method with the solution obtained based on the Finite Element Method (FEM) using ANSYS®. A parametric study is then conducted to investigate the influences of taper configurations and taper parameters on the free vibration response of the composite plates.